It has been known in practice that the cover films, which are stretched above and below between the pressed bale and the pressure rams, are wrapped by pins and placed on the lateral surfaces of the pressed bale after the press box has been pulled off. If desired, a belly band is placed around the bale, and the package is finally fixed by straps. The relatively inaccurate wrapping with the cover film has proved to be disadvantageous in practice, because the usually rectangular cover film, which projects beyond the base of the bale on all sides, is crumpled in the corners in an undefined manner, and it may become detached, despite strapping, when the pressed bale expands after releasing the pressure exerted by the pressure rams or later, during storage. As a result, the bale package may open, as a consequence of which the pressed bale will be exposed to environmental effects, such as soiling, rain water, etc., in an undesired manner.